Minimal perfect hash functions are used for memory efficient storage and fast retrieval of items from static sets. We present an infinite family of efficient and practical algorithms for generating order preserving minimal perfect hash functions. We show that almost all members of the family construct space and time optimal order preserving minimal perfect hash functions, and we identify the on...

A secure hash structure in Random Oracle Model may not be a secure model in true design. In this paper, we give an integrated proof method on security proof of iterated hash structure. Based on the proof method, we can distinguish the security of Merkel-Damag̊ard structure, wide-pipe hash, double-pipe hash and 3c hash and know the requirement of true design on compression function, and give a ne...

In a recent paper, A. Joux [7] showed multicollision attacks on the classical iterated hash function. (A multicollision is a set of inputs whose hash values are same.) He also showed how the multicollision attacks can be used to get a collision attack on the concatenated hash function. In this paper, we first try to fix the attack by introducing a natural and wide class hash functions. However,...

In this paper, we propose a secure Hash Algorithm with the focus on Data Integrity. A hash function, is a function that takes some message of any length as input and transforms it into a fixed-length output called a hash value, in DILH the hash value length 1152 bits. Many types of hash functions have been defined but, the most widely used in many of the cryptographic applications currently are...

We present a new polar representation of quaternions inspired by the Cayley-Dickson representation. In this new polar representation, a quaternion is represented by a pair of complex numbers as in the Cayley-Dickson form, but here these two complex numbers are a complex ‘modulus’ and a complex ‘argument’. As in the Cayley-Dickson form, the two complex numbers are in the same complex plane (usin...

Nathanson was the pioneer in introducing the concepts of Number Theory, particularly, the "Theory of Congruences" in Graph Theory, thus paving way for the emergence of a new class of graphs, namely "Arithmetic Graphs". Cayley graphs are another class of graphs associated with the elements of a group. If this group is associated with some arithmetic function then the Cayley g...

Cryptographic hash functions are important cryptographic techniques and are used widely in many cryptographic applications and protocols. All the MD4 design based hash functions such as MD5, SHA-0, SHA-1 and RIPEMD-160 are built on Merkle-Damgård iterative method. Recent differential and generic attacks against these popular hash functions have shown weaknesses of both specific hash functions a...